On the numerical rational connectedness of the Hilbert schemes of 2-points on rational surfaces
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We prove that the Hilbert schemes of 2-points on rational surfaces are numerically rationally connected. The main idea is to show that certain 3-point genus-0 Gromov–Witten invariant of the Hilbert scheme of two points on the complex projective plane is positive and can be calculated enumeratively.
Mathematics Subject ClassificationPrimary 14M22 14C05 Secondary 14N35 53D45
The authors would like to thank Professors Dan Edidin, Wei-Ping Li and Qi Zhang for stimulating discussions and valuable helps. The authors also would like to thank the referee for carefully reading the paper and providing valuable comments which have greatly improved the exposition of the paper.
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